A simplified model of a motorcycle traveling over a rough road is shown in Fig. 14.31. It is assumed that the wheel is rigid, the wheel does not leave the road surface, and the cycle moves at a constant speed \(v\). The cycle has a mass \(m\) and the suspension system has a spring constant \(k\) and a damping constant \(c\). If the power spectral density of the rough road surface is taken as \(S_{0}\), find the mean square value of the vertical displacement of the motor cycle (mass, \(m\) ).

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m k/2k/2 FIGURE 14.31 Simplified model of motor cycle on rough road.